However, calcification by corals reared under elevated nutrients combined with elevated CO2 was not significantly different from that of corals reared under ambient conditions, suggesting that CO2 enrichment can lead to nutrient limitation in zooxanthellate corals.

Nutrient limited corals are unable to utilize an increase in dissolved inorganic carbon (DIC) as nutrients are already limiting growth, thus the effect of elevated CO2 on saturation state drives the calcification response. Under nutrient replete conditions, corals may have the ability to utilize more DIC, thus the calcification response to CO2 becomes the product of a negative effect on saturation state and a positive effect on gross carbon fixation, depending upon which dominates, the calcification response can be either positive or negative.

And from the article, also minimally edited for clarity:

[…]the saturation state of the surrounding seawater alone does not control coral calcification as corals can continue to calcify in under-saturated conditions (e.g. Marubini and Atkinson, 1999; Cohen et al., 2009) or dissolve in super-saturated conditions (e.g. Herfort et al., 2008).